COSC 49.12 Topics in Computational Topology
Planar graphs are among the most well-studied graph classes since the beginning of graph theory and algorithm design. Planar graphs can manifest in computational problems as networks, meshes, or terrains that are geometric and low-dimension in nature, which unsurprisingly find many applications in computer graphics, visualization, vehicle routing, and shape analysis. This graduate-level seminar-style course is aimed to introduce a vast array of tools for planar graphs, ranging from combinatorial to geometric to spectral to algorithmic and beyond. Naturally, due to the sheer amount of work and literature in the area, the topics covered in this class will be biased towards the interest and expertise of the instructor.